Care tutte e cari tutti,

Ricordiamo il seminario di domani, giovedì 31 ottobre, alle 17 in Sala Seminari, "Evolution of gaussian fields by the flow of the nonlinear Schrödinger equation" di Nikolay Tzvetkov (École Normale Supérieure de Lyon). Trovate l'abstract qui sotto. Attenzione all'aula, diversa dal solito.

A presto, Ilaria Lucardesi e Luigi Forcella.

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Deal all,

We remind you the seminar "Evolution of gaussian fields by the flow of the nonlinear Schrödinger equation" by Nikolay Tzvetkov (École Normale Supérieure de Lyon), tomorrow, thursday 31st october, at 5p.m. in Sala Seminari. Pay attention to the room: it is not the usual one! Please, find the abstract here below.

Best wishes, Ilaria Lucardesi e Luigi Forcella.

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Speaker: Nikolay Tzvetkov (École Normale Supérieure de Lyon) Title: Evolution of gaussian fields by the flow of the nonlinear Schrödinger equation Abstract: We will discuss the non linear Schrödinger equation with data distributed according to gaussian fields. These fields are invariant under the free evolution and the question is how much the non linear interaction affects the invariance property. We will present a recent result, obtained in collaboration with Chenmin Sun, showing that for the three dimensional energy critical problem the law of the solution at any time is absolutely continuous with respect to the law of the initial gaussian field. We are therefore in slightly out of equilibrium regime. It should be emphasized that, thanks to the work by Aizenman and Duminil-Copin, we do not expect to reasonably define a Gibbs measure for an energy critical problem. Therefore the consideration of general gaussian fields becomes even more natural. The main new idea is the use of a cancellation of (probabilistically) resonant contributions in a modified energy estimate. We also rely on several techniques developed in recent years in the field of probabilistic well-posedness of dispersive PDE's. We will overview these ideas and techniques.